# Dynamics of a Mechanical System with Multiple Degrees of Freedom out of Thermal Equilibrium

## TL;DR

This paper develops a first-principles framework to calculate forces and responses in mechanical systems with multiple degrees of freedom out of thermal equilibrium, revealing how environments influence steady states and stability.

## Contribution

It introduces a method to derive forces, potentials, and kinetic equations for complex mechanical systems beyond thermal equilibrium, extending statistical physics models.

## Key findings

- Effective potentials can be created by environments near thermal equilibrium.
- Stable and unstable rectifications of thermal fluctuations are demonstrated.
- Steady state stability depends on chiral symmetry.

## Abstract

Out of thermal equilibrium, an environment imposes effective mechanical forces on microscopical nanofabricated devices, chemical or biological systems. Here we address the question of how to calculate these forces together with the response of the system from the first principles. We show that an ideal gas-like environment, even near thermal equilibrium, can enforce a specific steady state on the system by creating effective potentials in otherwise homogeneous space. An example of stable and unstable rectifications of thermal fluctuations is presented using modified Feynman-Smoluchowski ratchet with two degrees of freedom. Moreover, the stability of a steady configuration depends on its chiral symmetry. The transition rate probabilities and the corresponding kinetic equations are derived for a complex mechanical system with arbitrary degrees of freedom. This work therefore extends the applicability of mechanical systems as a toy model playground of statistical physics for multiple degrees of freedom active and living matter.